Algebra & Number Theory

Algebraic de Rham theory for weakly holomorphic modular forms of level one

Francis Brown and Richard Hain

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Abstract

We establish an Eichler–Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. This leads to formulae for the periods and quasiperiods of modular forms.

Article information

Source
Algebra Number Theory, Volume 12, Number 3 (2018), 723-750.

Dates
Received: 3 August 2017
Revised: 22 December 2017
Accepted: 22 January 2018
First available in Project Euclid: 28 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.ant/1532743369

Digital Object Identifier
doi:10.2140/ant.2018.12.723

Mathematical Reviews number (MathSciNet)
MR3815311

Zentralblatt MATH identifier
06890766

Subjects
Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F23: Relations with algebraic geometry and topology 11F25: Hecke-Petersson operators, differential operators (one variable) 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Keywords
weakly holomorphic modular form algebraic de Rham cohomology

Citation

Brown, Francis; Hain, Richard. Algebraic de Rham theory for weakly holomorphic modular forms of level one. Algebra Number Theory 12 (2018), no. 3, 723--750. doi:10.2140/ant.2018.12.723. https://projecteuclid.org/euclid.ant/1532743369


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